Problem: The arithmetic sequence $(a_i)$ is defined by the formula: $a_1 = 2$ $a_i = a_{i-1} + 2$ What is $a_{4}$, the fourth term in the sequence?
From the given formula, we can see that the first term of the sequence is $2$ and the common difference is $2$ To find the fourth term, we can rewrite the given recurrence as an explicit formula. The general form for an arithmetic sequence is $a_i = a_1 + d(i - 1)$ . In this case, we have $a_i = 2 + 2(i - 1)$ To find $a_{4}$ , we can simply substitute $i = 4$ into the our formula. Therefore, the fourth term is equal to $a_{4} = 2 + 2 (4 - 1) = 8$.